Don't think of tankers just as range extenders, think of them as force multipliers.
If I have a CAP 1 hour from base with 1 hour on task and a 1 hour turn, then 8 aircraft are required to maintain a pair on station. But if I have a tanker allowing the TOT to be extended to 3 hours, then I only need 4, halving the required force or doubling the number on CAP.
The proximity of the carrier means aircraft can be rapidly rearmed once fired out, but even if flown from a remote base the tankers provide a massive boost in capability. Which is why the carrier based assets off the coast of Pakistan for Afghanistan Ops were supported by Oman based tankers and why the RAF in Bahrain supported USN FJ flying up from the Indian Ocean in GW1.